Diffusion and escape times in the open-leaky standard map

We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum coordinate vary freely and restrict only angle with periodic boundary condition. We also define a pair of artificial holes placed symmetrically along the momentum axis where the particles might leave the system. As a consequence of the leaks the diffusion can be analyzed making use of only the ensemble of survived particles. We present how the diffusion coefficient depends on the size and position of the escape regions. Since the accelerator modes and, thus, the diffusion are strongly related to the system's control parameter, we also investigate effects of the perturbation strength. Numerical simulations show that the short-time escape statistics do not follow the well-known exponential decay especially for large values of perturbation parameters. The analysis of the escape direction also supports this picture as a significant amount of particles skip the leaks and leave the system just after a longtime excursion in the remote zones of the phase space.

[Meta-analysis of therapeutic and preventive clinical trials]

The paper surveyes the principles and the models of meta-analysis and gives the basic statistical formulae. For evaluation of data of clinical trials two illustrative examples are presented: 1. evaluation of association and homogeneity in fixed and random models of the common standardized treatment effects measured by continuous variable with known sample sizes, means and standard deviations; 2. evaluation of association and homogeneity in fixed model of: the common InRelative-Risk and Risk-Difference ot treatment effects determined by dichotomous variable categorized in 2 x 2 tables and completed with Stouffer and Fisher methods combining z and p values of percentage differences of the treatment effects. It is demonstrated that the presented two illustrative examples, as models of meta-analysis provide objective statistical methods for data summarization of clinical trials. Evidence based medicine applies also the methods of meta-analysis.

[Evaluation of medical diagnostic tests: application of Bayes theorem, ROC-curve and Kappa-test]

With the technical improvement of the sensitivity and specificity of the medical diagnostic tests the principles and methods of statistical analysis of the tests are in developing too. The technical development of the diagnostic tests and the exact statistical evaluation of the data will improve the reliability and effectiveness of the decisions for medical interventions. Application, statistical evaluation and interpretation of the Bayes theorem, ROC curve and Kappa test are presented.

[Statistically validated evaluation of clinical trials]

Data of clinical trials of medicinal products must be evaluated in statistically valid models. The statistical validity criteria are defined. Statistically invalid models will result in biased parameter and confidence interval estimations, erroneous statistical inferences and clinical interpretations. Finally, wrong decisions will call forth deleterious consequences in the judgement of the therapeutic effect and the frequency and severity of the adverse reactions of the tested new medicinal, and generic products. Statistically validated analyses will promote the international harmonization of the scientific evaluation of medicinal products according to the idea of the evidence-based-medicine. The study presents examples of clinical trials evaluated with a software checking statistical validity assumptions while performing evaluation of data.

[Results of the BCG vaccination in Hungary since 1929: evaluation of preventive and immunotherapeutic effectiveness]

BACKGROUND

The BCG (Bacille Calmette-Guérin), a living attenuated bacterial vaccine with a characteristic residual virulence, has been used to prevent tuberculosis since 1921 (in Hungary non-systematically since 1929) and applied for immunostimulation in neoplasia since the 1960s.

MEASURES

Considering the grave tuberculosis epidemiological situation in Hungary, the BCG revaccination became compulsory up to 20 years old tuberculin negatives since 1959. The Pasteur P1173P2 BCG strain has been used for vaccine manufacturing with improved quality control methods according to the requirements of the WHO. With in systematic BCG primo and revaccination policy 8.1 million BCG vaccination from 1959 to 1983 then further 3.1 million between 1984 and 1996 have been performed.

RESULTS

Linear regression analysis demonstrates that the decrease of the TB incidence in children was 3-5 times more rapid (annual average decrease was 25.5%) than in adult since 1959. Multiple regression analysis indicates that the BCG is the strongest explanatory variable decreasing children TB incidence among other antituberculosis measures. The BCG vaccination efficacy ins demonstrated by 2 x 2 table analysis. The systematic BCG vaccination, the living and persisting BCG in the macrophages, confers acquired resistance against virulent TB infections. The immunostimulation in neoplasia has been applied with concentrated BCG developed in Hungary since 1979. The adverse reactions are at accepted frequency. The number of BCG vaccinated subjects was estimated at 1.5 billion from 1948 to 1974 in the world. The yearly number of BCG vaccination in the WHOI-EPI System is estimated 50-100 million.

CONCLUSION

The efficacy of the BCG vaccination can only be ensured if the vaccine is manufactured and controlled with standardized methods, and applied in a systematic vaccination programme. The effectiveness has to be evaluated in statistically valid biostatistical models.

Theoretical and methodological aspects of BCG vaccine from the discovery of Calmette and Guérin to molecular biology. A review

The BCG vaccine has been used to prevent tuberculosis since 1921 and applied for immunostimulation in neoplasia since the 1960s. Both the preventive and immunostimulation effects have been evaluated and communicated with contradictory, positive and negative conclusions. For an objective evaluation and interpretation of the protective efficacy, effectiveness and efficiency of the BCG vaccination it must be considered that: (1) several BCG substrains have been developed in manufacturing laboratories that differ in the residual virulence which determines immunogenicity and reactogenicity; (2) various liquid and freeze-dried BCG vaccine production methods are used, resulting in different BCG viable units per dose; (3) quantitative bioassay methods are not yet being used for statistical quality control of the vaccine; (4) BCG products are applied in various demographical, epidemiological and socioeconomic conditions with different vaccination policies; (5) inadequate biostatistical models are often used to analyse efficacy, effectiveness and adverse reactions. The same conditions influence the precise evaluation of BCG immunostimulation in neoplasia. Recombinant DNA technology will modify production methods, and explain at the molecular level the mechanism of the protective effects BCG confers in tuberculosis and immunostimulation in neoplasia. High level laboratory techniques and biostatistical methods, based on probability logic and inductive inference, ensure appropriate experimental designs and the exact analysis of laboratory data and the results of vaccination policies. They will lead to the evaluation of the protective effect of BCG in order to reduce the BCG contradictions.

Relative persistence capacity of BCG substrains in mouse spleen. Computerized statistical analysis. Multiple comparison

The relative persistence capacity in mouse spleen of 10 and 9 BCG substrains from liquid and dried vaccines, respectively, was evaluated in two studies. Recoverable BCG colony counts from mouse spleen were determined at given days on solid medium in the two studies during a period of 1-360 and 1-345 days, respectively, after the intravenous BCG vaccination, performed with two different viable units. From 36,000 (study 1) and 21,600 (study 2) recoverable BCG colony counts, 180 and 108 mean relative persistence capacity values were estimated to test the residual virulence during the follow-up time, using computerized statistical analysis. The early and late trends of mean relative persistence capacity of the BCG substrains in mouse spleen were tested by linear regression analysis and analysis of variance and covariance; then with ranked adjusted group mean relative persistence capacity, Gabriel's simultaneous test procedure was performed for multiple comparison to diminish type 1 error in statistical inference and in objective interpretation of the experimental results. The associations of the ranked mean relative persistence capacity of the BCG substrains at the different sacrifice days of mice were also analyzed by Kendall's test of concordance. The early, late, and overall relative persistence capacity reflects the residual virulence of the BCG substrains and provides information on the required protective efficacy (immunogenicity) and adverse reactions (reactogenicity), allowing the appropriate vaccination dose, expressed in viable units of the substrain used, to be determined.

Biostatistical manual (BIOSTAT) for potency control and for evaluation of effectiveness of the WHO-EPI vaccines: software for personal computers

In accordance with WHO requirements, a specialized software has been developed for personal computers to analyse the potency data of the EPI vaccines and to evaluate the effectiveness of the vaccination. The software has three parts and allows users to create files from control data (BIOSTAT), to check the function of the software and statistical formulae (BIOSDEMO), and to understand the logic and structure of the data processing system and the statistical models (BIOSDOC).

Analysis of variables of plasmid transformation of a bacterial vaccine: studies on recombinant BCG

Stepwise regression analysis was applied to evaluate the strength order of the effect of five explanatory variables on the transformation of BCG substrains by electroporation with hybrid shuttle plasmid [pAL5000:pIJ666] and derived as YUB plasmids containing a kanamycin resistance selection marker. From 66 successful transformations, data of 42 transformations of the Pasteur 1172P2 BCG substrain are analysed. The estimated parameters in the multiple linear regression model show that the association of the explanatory variables with the explained variable, i.e. the efficiency of the transformation of BCG expressed in c.f.u./microgram DNA, in decreasing strength order is: concentration of the plasmid DNA; viability of the non-electroporated concentrated BCG suspensions; viability of the BCG cultures; age of the BCG cultures; and time constant of the electroporation. More extended analysis of other factors of the transformation will improve objective statistical inference regarding the biophysical and molecular biological interpretation of the transformation mechanism by electroporation of the different bacterial species. More precise understanding of optimal conditions of genetic transformation will be particularly important for developing recombinant BCG vaccines.

Transport and storage of vaccines in Hungary: the first cold chain monitor study in Europe

With assistance from WHO the Hungarian Ministry of Health organized two cold chain studies: the first in three counties in summer (1 July to 30 September 1987), the second in six counties (including the previous three) in winter (1 January to 31 March 1988). The counties were chosen according to their distance (50-300 km) from Budapest, individual districts and child health centres being selected randomly. All participants were trained before beginning the studies. The vaccines (DPT, measles and BCG) for immunization, with attached cold chain monitors, were transported from the manufacturers to the child health centres using the normal distribution systems in the country. The whole cold chain process was analysed with regard to (1) actual exposures to adverse temperatures and delays in distribution; (2) the places where such exposure or delay occurred; (3) the percentage of vaccines at risk of deterioration (actual and predicted) at the end of the study; and (4) the performance of refrigerators of different types. Evaluation of the results (using WHO's EPIC software) showed significant deviations from acceptable standards. This first cold chain study in a European country proves that even in a temperate climate and with a reasonably well-organized public health service there can be significant weaknesses in the transportation and storage of vaccines. Recommendations to overcome these deficiencies are given.

Genetic transformation of BCG

Two substrains of BCG, the Pasteur and Japanese, were successfully transformed with E. coli-mycobacteria shuttle plasmids, constructed from the E. coli plasmid, pIJ666 and the M. fortuitum plasmid, pAL5000. Individual plasmids (pYUB13, pYUB14) were obtained that contain selectable antibiotic resistance markers for kanamycin and chloramphenicol resistance that can replicate in both E. coli and BCG. Transformation of two substrains of BCG was successfully accomplished in 8/14 experiments by means of electroporation, and assessed by the growth of kanamycin-resistant colonies. The E. coli plasmid pIJ666 alone was unable to effect transformation. The results suggest that the M. fortuitum sequences required for transformation function as an origin of replication in BCG. The introduction, persistence and the identity of the plasmids were monitored by re-isolation from consecutive subcultures and restriction analysis. The variables associated with transformation, including the age, viability, and glycine pretreatment of BCG cultures, as well as the electroporation parameters on transformation frequencies are analysed. Consecutive transformations of BCG with plasmid DNA isolated from a BCG transformant increased the efficiency from the level of 10(1)-10(2) obtained with the initial library to 10(3)-10(4) colonies/micrograms DNA with functional pYUB plasmids. The hybrid plasmids were genetically stable and maintained expression of kanamycin resistance in continuous subcultures containing kanamycin for 250 generations. The introduction and stable expression of foreign DNA in BCG on a plasmid vector establishes a basis for the construction of polyvalent recombinant BCG vaccine vehicles expressing not only putative protective mycobacterial antigens, but also antigens for other infectious and malignant diseases.

Lysogeny and transformation in mycobacteria: stable expression of foreign genes

Requisite to a detailed understanding of the molecular basis of bacterial pathogenesis is a genetic system that allows for the transfer, mutation, and expression of specific genes. Because of the continuing importance of tuberculosis and leprosy worldwide, we initiated studies to develop a genetic system in mycobacteria and here report the use of two complementary strategies to introduce and express selectable genetic markers. First, an Escherichia coli cosmid was inserted into the temperate mycobacteriophage L1, generating shuttle phasmids replicating as plasmids in E. coli and phage capable of lysogenizing the mycobacterial host. These temperate shuttle phasmids form turbid plaques on Mycobacterium smegmatis and, upon lysogenization, confer resistance to superinfection and integrate within the mycobacterial chromosome. When an L1 shuttle phasmid containing a cloned gene conferring kanamycin resistance in E. coli was introduced into M. smegmatis, stable kanamycin-resistant colonies--i.e., lysogens--were obtained. Second, to develop a plasmid transformation system in mycobacteria, M. fortuitum/E. coli hybrid plasmids containing mycobacterial and E. coli replicons and a kanamycin-resistance gene were constructed. When introduced into M. smegmatis or BCG (Mycobacterium tuberculosis typus bovinus var. Bacille-Calmette-Guérin) by electroporation, these shuttle plasmids conferred stable kanamycin resistance upon transformants. These systems should facilitate genetic analyses of mycobacterial pathogenesis and the development of recombinant mycobacterial vaccines.

Trends in childhood tuberculosis in Hungary 1953-1983: quantitative methods for evaluation of BCG policy

To analyse the effectiveness of the BCG policy on childhood tuberculosis in Hungary, the following three quantitative methods have been organized and systematically applied since 1959; regression analysis with multiple comparison of the incidence trends of age groups; stepwise regression analysis to select the strongest childhood incidence decrease factor; and a log-linear model to compare the risk of disease in vaccinated and non-vaccinated children. The increasing BCG coverage of children as a specific antituberculous measure (i) has decreased the childhood incidence (23-32% per year) 3-4 times more rapidly than the adult incidence (6-16% per year) as shown by the regression analysis, (ii) has acted as the strongest incidence decrease effect among other factors and (iii) has protected the vaccinated children 2.8 times better than the non-vaccinated ones. The use of valid and exact models, from statistical inferences ensure the objective interpretation of the epidemiological events in tuberculosis.

Multiple comparison of dried BCG vaccines: stability at 37 degrees C and persistence of strains in the mouse spleen

The Gabriel test was used for multiple comparison of the stability of vaccines stored at 37 degrees C over a 28 day period and of the long-term relative persistence capacity (RPC) in mice spleen (residual virulence) over a 547 day period following intravenous vaccination with 12 BCG dried products. Multiple comparisons were performed after rejected null hypotheses (Anova, Regranal), with ranked mean viable units 10(6) ml-1 estimates (VU) of vaccines and with ranked mean RPC values in spleen determined with five sampling and on nine autopsy days, respectively. Results showed that VU X 10(6) ml-1 values of the compared vaccines at day 0 varied between 1.1 and 27.0 X 10(6) ml-1 and formed two homogeneous subsets. The heat stability test showed that the VU X 10(6) ml-1 values of the vaccines decreased parallely but at day 28 only six vaccines showed a survival rate over 20%. The RPC model showed that the trends of early multiplication and of late persistence capacity depended on the i.v. BCG VU doses. The Regranal of late RPC indicated that the decrease of BCG VU in mice spleen from 84 to 547 days was parallel and that six strains persisted over 20% at day 360. The overall RPC on the nine autopsy days of the BCG strains was evaluated with Kendall concordance test. In contrast with pairwise comparison, the Gabriel test reduces the risk of type I error in statistical inference at the 5% experimental level and selects the homogeneous subsets of ranked parameter estimates of the compared products.(ABSTRACT TRUNCATED AT 250 WORDS)

Control of viability, thermostability and residual virulene of BCG vaccines. Multiple comparison of laboratory data to select products for immunostimulation in the treatment of cancer

The aid of the work was to apply the multiple comparison method to select BCG products for immunostimulation. In the IABS-BCG Collaborative Study 1973 program coded BCG products (code) and reference preparation were investigated with 3 laboratory tests to compare differences concerning: (1) viability = viable units E6/ml (VU) of vaccines stored at 4C, (2) 37C thermostability (TS) slope = daily VU decrease of vaccines stored at 37C/0, 7, 14, 21, 28 days, (3) relative persistence capacity (RPC),--residual virulence--of the BCG strains in the mice spleen; regression followed up to 360 days. Culturable particles and recoverable VU were determined on BOAA medium. Means and regression coefficients of VU, TS and RPC were ranked after analysis of variance and evaluated by multiple-comparison-Gabriel method. Figures summarize the results. As to VU the products form 3 subsets; as to TS the products are in two subsets (ie potency of several products could be included in the same subset). Thus, the ranks of VU and TS are not the same. Also there are differences among overall rank of RPC (coefficient concordance of ranks of 2 VU doses, log and sqrt transformation of exp. data) and the VU as well as the TS.

CONCLUSION

parallel VU, TS and RPC investigations and multiple comparison method could ensure the validity and reliability of the estimations in the quality control of products for immunostimulation and could explain the correlations and contradictions between the laboratory data and the results of the clinical trial in neoplasia.